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Healthcare Finance and Budgeting, Statistics Problem Example

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Statistics problem

The following exercises are designed to help you practice the financial calculations that may be required of you in your managerial role. These exercises also allow you to demonstrate your learning thus far in this course.

For each problem:

  • State your answer in numerical terms
  • Explain in a narrative statement how you calculated your answer
  • Provide an original example/scenario that demonstrates your understanding of the concept and requires you to calculate the answer using a separate set of figures

Average Daily Census and Occupancy Rate and Average Length of Stay

Assume a 40-bed medical-surgical inpatient unit has 12,000 patient days per year based on 1,050 annual admissions. What is the ADC (average daily census)? What is the occupancy rate? What is the ALOS (average length of stay)?

Your answer in numerical terms:

Average Daily Census =12,000/365=32.87                            

Occupancy rate= 32.9/ 40 = 82.25%

ALOS= 12,000/1,050 = 11.42 days- average length of stay

Narrative statement that explains how you calculated your answer:

There are three different answers calculated for the problems above. 

The ADC refers to the average of the inpatient days/ number of days; the occupancy rate refers to average occupancy of the hospital;

ALOS is measuring the average length of stay among those who were in the hospital. 

Original example/scenario that demonstrates your understanding and includes your calculations using a separate set of figures:

30 beds- 9000 patient days- 500 annual admissions

ADC= 9000/365= 24.65

Occupancy rate= 24.65/30= 82.1%

ALOS= 9000/500=18

Staffing Requirements and Full-time Equivalents

Assume that a home health agency requires 6,000 nursing care hours. If a full-time equivalent (FTE) is paid for 2,080 hours and nonproductive hours are 382 per FTE, how many FTEs will be required to provide the required care hours?

Your answer in numerical terms:

2080 productive hours- 383 non-productive hours= 1697 hours

=6000/1697= 3.53 FTE

Narrative statement that explains how you calculated your answer:

The required hours (6000) would require 3.53 individuals working full time

Original example/scenario that demonstrates your understanding and includes your calculations using a separate set of figures:

An agency requires 8000 hours; a FTE is paid for 2000 hours

This agency would require 4 FTEs.

 Staffing Requirements and Full-time Equivalents (continued)

Assume the agency in the above example operates a total of 250 days a year. How many care hours must it provide per day? Assuming 8-hour shifts and using only registered nurses, how many nurses must be on duty each day?

Your answer in numerical terms:

6000 total hours/250 total days of operation= the agency must provide 24 care hours a day

= 24/8 at least 3 nurses must be on shifts per day

Narrative statement that explains how you calculated your answer:

In order to solve the problem, I took the total hours needed for operation divided by the number of days in a year that the agency operates.  I then took the answer from that (24 hours per day) divided by the 8-hour shifts needed to get the answer 3 nurses per day.

Original example/scenario that demonstrates your understanding and includes your calculations using a separate set of figures:

300 days a year assuming 6 hour shifts for RNs, 2Rns ?

 6000/ 300= 20 total hours of care

6 hour shifts for 2 RNs-

=20/12= 1.25

Calculating Workload

Assume that a clinic expects to have 5,000 visits next year. It expects the visits to be divided equally among each of the four general types of patients. The required care for the four types of patients is 0.5 hours, 0.8 hours, 1.2 hours, and 2 hours, respectively.

What is the total workload in care hours? What are the expected care hours per clinic visit?

 Your answer in numerical terms:

Total visits= 5,000

 Type 1) 1,250 visits *.5=    625  hours

Type 2) 1,250 visits *.8 = 1,000 hours

Type 3) 1,250 visits *1.2= 1,500 hours

Type 4) 1,250 visits *2    = 2,500 hours

 = 5,625 hours

 =5,625/5000= 1.125 hours per clinic visit

Narrative statement that explains how you calculated your answer:

I divided the 5,000 total predicted visits equally over four “types” of patients- I then applied the time differential per type of patient to come up with a total expected clinic time of 5,625. 

I then took total hours (5,625) divided by total visits to get the average predicted time per clinic visit.

Original example/scenario that demonstrates your understanding and includes your calculations using a separate set of figures:

10 0000 visits over 4 types with types of care needed equal to 4 hours, 3 hours, 2 hours, and 1  hou5

 Type 1) 2,500*4= 10,000

Type 2) 2,500*3 = 7,500

Type 3) 2500*2 = 5,000

Type 4) 2500*! = 2,500

 =25,000/10,000 visits= 2.50 hours per visit

Accounts Receivable

Suppose that a healthcare organization had revenues of $300,000 for March and that the payer mix is as follows:

Payer Percent of Patients Payment Lag
Medicare 40 3 months
Medicaid 20 3 months
Blue Cross 15 2 months
Other insurer 15 1 month
Self-pay 10 2 months

How much cash will be received in May from March revenues? Will that be all the revenue received that month?

Your answer in numerical terms:

$ 75,000 will be received in May; this is because this is the amount related to the payers who will pay in two months, or 25% of total revenue.  Yes, this is the only money that will be received in May.  The other monies will come in during May,

Narrative statement that explains how you calculated your answer:

I took the number of months that would be received during the month. 

Original example/scenario that demonstrates your understanding and includes your calculations using a separate set of figures:

Payer Percent of Patients Payment Lag
Medicare 20 3 months
Medicaid 20 3 months
Blue Cross 20 2 months
Other insurer 20 1 month
Self-pay 20 2 months

60 percent of revenue will be received; yes that will be received per month.

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